permanent
Continuing, uninterrupted, or remaining for a long time; lasting.
Wegen des Wasserschadens ist die Straße permanent gesperrt.
Because of the water damage, the road is permanently closed.

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Continuing, uninterrupted, or remaining for a long time; lasting.
Wegen des Wasserschadens ist die Straße permanent gesperrt.
Because of the water damage, the road is permanently closed.

'Permanent' can stand as an adjective before a noun, describe a verb as an adverb, or be used with 'sein' (to be). This flexibility makes it very useful in formal contexts.
Wir suchen eine permanente Lösung für das Problem.
We are looking for a permanent solution to the problem.
Be careful with hairstyles: a perm, often called a 'perm' or 'permanent wave' in English, is called 'die Dauerwelle' in German, not 'die Permanente'.
Sie hat sich beim Friseur eine Dauerwelle machen lassen.
She got a perm at the hairdresser's.
The word is often combined with states or situations. Typical collocations are 'permanenter Stress' (permanent stress), 'permanente Überwachung' (permanent surveillance), 'eine permanente Ausstellung' (a permanent exhibition), or 'permanent verfügbar sein' (to be permanently available).
Durch seine Arbeit steht er unter permanentem Stress.
Because of his work, he is under permanent stress.
'Permanent' belongs more to written language or to a more formal style. It often sounds more objective and technical.
Die Datenbank wird permanent aktualisiert.
The database is updated permanently.
constant
'ständig' and 'permanent' can both express that something lasts a long time or happens very often. 'ständig' is very common in everyday language and fits repeated things well, for example 'ständige Fragen' (constant questions) or 'ständige Probleme' (constant problems). 'permanent' sounds a bit more formal and emphasizes more strongly that something remains lasting or uninterrupted. Learners may confuse the words because both come close to 'immer' (always). For normal everyday situations, 'ständig' is often more natural. 'permanent' is more suitable when a state remains for a longer time or feels very fixed.

Nach dem Unfall hat sie permanente Schmerzen im Rücken.
After the accident, she has permanent pain in her back.
Vor dem Wochenende kommen ständig neue E-Mails von Kunden.
Before the weekend, new emails from customers keep coming in.